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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 2, 1983, pp. 145–157
DOI: 10.4171/ZAA/56

Published online: 1983-04-30

Zur Konvergenz von Iterationsverfahren mit affinen Operatoren

Dieter Schott[1]

(1) Hochschule Wismar, Germany

Many well-known numerical procedures for the iterative solution of linear equations in Banach spaces have the form $$x_{n+1} = \mathbf A_n \mathbf A_{n-1} \dots \mathbf A_0x_0 (n = 0, 1, 2, \dots)$$ with affine operators $\mathbf A_n$. If the operators $\mathbf A_n$ possess common fixed points, then there often exist affine projectors $\mathbf P$ with the property $$\mathbf P = \mathbf A_n \mathbf P = \mathbf {PA}_n \quad (n= 0, 1,2, \dots).$$ In this paper some convergence theorems are proved for iteration methods having such operator sequences.

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Schott Dieter: Zur Konvergenz von Iterationsverfahren mit affinen Operatoren. Z. Anal. Anwend. 2 (1983), 145-157. doi: 10.4171/ZAA/56